Nilpotent injectors in finite groups

In [3] A. Bialostocki has introduced a special class of maximal nilpotent subgroups in an arbitrary finite group. ¶In this paper we want to investigate the relationship between this special class of maximal nilpotent subgroups and the more classical \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\cal N $\end{document}-injectors in an arbitrary finite group. ¶To do this we prove the following theorem which is of fundamental importance in this investigation: ¶Let U be a nilpotent subgroup of G containing every U-invariant nilpotent subgroup of G. Then U is an $\cal N $-injector of G.